6(8x-3)(2x+1)=0

Solution for 6(8x-3)(2x+1)=0 equation:

Simplifying
6(8x + -3)(2x + 1) = 0

Reorder the terms:
6(-3 + 8x)(2x + 1) = 0

Reorder the terms:
6(-3 + 8x)(1 + 2x) = 0

Multiply (-3 + 8x) * (1 + 2x)
6(-3(1 + 2x) + 8x * (1 + 2x)) = 0
6((1 * -3 + 2x * -3) + 8x * (1 + 2x)) = 0
6((-3 + -6x) + 8x * (1 + 2x)) = 0
6(-3 + -6x + (1 * 8x + 2x * 8x)) = 0
6(-3 + -6x + (8x + 16x2)) = 0

Combine like terms: -6x + 8x = 2x
6(-3 + 2x + 16x2) = 0
(-3 * 6 + 2x * 6 + 16x2 * 6) = 0
(-18 + 12x + 96x2) = 0

Solving
-18 + 12x + 96x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + 2x + 16x2) = 0

Factor a trinomial.
6((-1 + -2x)(3 + -8x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(3 + -8x)' equal to zero and attempt to solve:

Simplifying
3 + -8x = 0

Solving
3 + -8x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -8x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8x = 0 + -3
-8x = 0 + -3

Combine like terms: 0 + -3 = -3
-8x = -3

Divide each side by '-8'.
x = 0.375

Simplifying
x = 0.375
Solution
x = {-0.5, 0.375}